Method utilizing brewster angle for determining angular velocity and light beam incidence angles

ABSTRACT

A light beam linearly polarized in its plane of incidence is projected onto the peripheral surface of a rotably refracting disc at an angle that effects absorption of all the incident light. Means for detecting reflected light are positioned proximate to the point of incidence. Angular velocity of the disc is determined by the amount of change in angle of incidence of the light beam required to eliminate any light reflected due to disc movement. Change in angle of incidence of the light beam is measured by rotating the disc to a speed that eliminates any light reflected due to such change in angle of incidence.

Elnited States Patent [191 Newburgh 51 May 22, 1973 {54] METHOD UTILIZING BREWSTER [56] References Cited ANGLE FOR DETERMINING UNITED STATES PATENTS ANGULAR VELOCITY AND LIGHT 3,355,980 12 1967 M th .356 118 BEAM INCIDENCE ANGLES a [75] Inventor: Ronald G. Newburgh, Belmont, Primary Examinerfikonald wibe" Mass Assistant ExaminerF. L. Evans Att0rney-Harry A. Herbert, Jr. et al. [73] Assignee: The United States of America as represented by the Secretary of the [57] ABSTRACT Force washmgton DC A light beam linearly polarized in its plane of inl Flledi g- 1971 cidence is projected onto the peripheral surface of a rotably refracting disc at an angle that effects absorp- [211 Appl' tion of all the incident light. Means for detecting reflected light are positioned proximate to the point of [52] US. Cl. ..356/27, 356/28, 356/114, in idence. Angular velocity of the disc is determined 356/118 by the amount of change in angle of incidence of the 51 lnt.Cl. ..G0lp 3/36 light beam required to eliminate y light reflected 58 Field of Search ..356/27 28, 114, due to disc movement Change in angle of incidence 3 5 6 ll 18 of the light beam is measured by rotating the disc to a speed that eliminates any light reflected due to such change in angle of incidence.

1 Claim, 2 Drawing Figures PATENTEDNAYZZIQB $734,619

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INVENTOR. RONALD G. NEWBURH W K) I METHOD UTILIZING BREWSTER ANGLE FOR DETERMINING ANGULAR VELOCITY AND LIGHT BEAM INCIDENCE ANGLES BACKGROUND OF THE INVENTION This invention relates to a novel application of the Brewster Angle phenomenon and particularly to apparatus and methods for determining angular velocity and light beam incidence angles.

There currently exists various applications wherein values indicating the relationship between angular rotation velocity and the angle of incidence of an impinging light beam can be put to practical use. For instance, precision calibration of rotating machinery can be accomplished by such a technique. Also remote monitoring of rotating devices such as may be employed in dangerous environmental test situations can advantageously be accomplished by means of Brewster angle devices. In the field of space navigation, the attitude relationship of a moving space vehicle with a light beam reference would be necessary information for successful guidance. Satisfacting means for acquiring such information are not now available. Accordingly, the present invention is directed toward providing methods and means for accomplishing these and other ends.

SUMMARY OF THE INVENTION The essential elements of the device of the present invention consist of a rotatable disc of refracting material, a light source capable of projecting a light beam that is linearly polarized in its plane of incidence, and means for detecting light reflected from the disc. In order to practice the invention as a means for measuring angular velocity the light beam is directed onto the periphery of the disc (while the disc is stationary) at an angle that produces no reflection. The disc is then rotated causing the Brewster angle conditions to be violated and concommitant reflection of the light beam. The light source is then moved to again achieve a no reflection condition. The amount of movement of the light source required to accomplish this is a direct measure of the angular velocity of the disc.

Determination of a change in angle of incidence of the light beam from an established reference angle is accomplished in a reverse manner. The disc (in a stationary condition) is initially positioned to intercept the light beam at the Brewster angle (no reflected light). Any detected reflected light by the light detecting means indicates a change in angle of incidence of the light beam. The disc is then rotated to a velocity that eliminates the reflected light. The disc velocity is measured and is a direct indication of the change in angle of incidence of the light beam.

It is a principal object of the invention to provide new and improved methods and means for relating the angular velocity of a rotatable disc to the angle of incidence of a light beam impinging thereon.

It is another object of the invention to provide new and improved methods and apparatus for measuring the angular velocity of rotating members.

It is another object of the invention to provide new and improved methods and apparatus for measuring the attitude deviation of a moving vehicle from a fixed reference light beam.

These together with other objects, advantages and features of the invention will become more apparent from the following detailed description when taken in conjunction with the illustrative embodiment in the accompanying drawings.

DESCRIPTION OF DRAWINGS FIG. 1 is a vector diagram illustrating the Brewster Angle Condition; and

FIG. 2 is an illustration of the organization of components necessary to practice the present invention.

DESCRIPTION OF PREFERRED EMBODIMENT If a ray linearly polarized in a plane of incidence is incident on a refractive medium at an angle whose tangent equals the relative index of refraction, there is no reflected ray and the refracted ray is perpendicular to the would-be reflected ray. This particular angle of incidence is called the Brewster angle. The observation of zero reflection is independent of the reference frame in which the observation is made. If all the energy in the incident ray enters the refractive medium, no observe in any frame can see a reflected ray. 1

The various quantities are shown in FIG. 1. Inciden light beam 15 having a polarization indicated by lines 14 is completely absorbed in the refracting medium as beam 13. Dashed line 12 indicates the would-be reflected beam (if the Brewster angle conditions were not met). The refractive medium occupies the region y 0 and is at rest in the'inertial frame K The frame K moves with velocity v in the positive x direction with respect to frame K Significant angles are designated as:

0 angle of incidence i1: angle of would-be reflection 5 angle of refraction.

The subscripts l and2 refer to quantities as measured by observers at rest in frames 1 and 2 respectively. For simplicity the incident ray'is propagated in vacuo (the region y O). The refractive medium is idealized by taking its dielectric constant n to be isotropic as for glass. As a further simplification the medium is considered to be non-dispersive so that the phase velocity and group velocity are equal. These idealizations simplify but do not change the conclusions hereinafter derived.

In frame K the proper frame of the refractive medium, the condition for zero reflection is tan 0 n or equivalently,

Equation (2) follows from Snell's law,

sin 0 /sin (b n Because of Equation (2), the following equation can be written an observer at rest in frame K the Lorentz transformations are applied to the wave number (4-vector (k,

iw/c), where k is the wave number in 3-space and w the angular frequency. The phase velocity IS always given as w/k. ln vacuo the phase velocity is and in the medium it is talk c/n.

The Lorentz transformations for k and k are where k, iw/c [3 v/c In terms of k,, k and w, the transformations are The results of the transformation are shown in the lowing Table 1.

fol-

The equivalent of Equation (4) for the frame K is tan 0 tan =0 y tan 0 cot B [l v/ (0 sin 0.)]

=7 [l v/ (6 sin 60].

For v 0, Equation (10) may be approximated as tan 0 tan 1+2v/(c sin 6,)+.

Equation l l differs from Equation (4) by a firstorder term in 2(v/c). Moreover, since sin 0, is always less than or equal to unity, its presence in the denominator ensures that 2(v/c) is the minimum value of the deviation. By applying the invariance of zero reflection for Brewster angle incidence a first-order effect in v/c is arrived at.

Referring now to FIG. 2, there is illustrated thereby an organization of components adapted to operate in accordance with the principle of the invention. Disc member 3 of refractory material is mounted on rotatable shaft ll. Shaft 11 can be rotated by any suitable means such as variable speed motor 9 and the belt and pulley system shown. A tachometer 10 is provided to measure the velocity of motor 9. Light beam 15 is provided by light source 4 which is mounted on frame member 7 and can be moved in the arc shown. Frame member 7 has calibration marks 8 suitable to accurately indicate any movement of light source 4. Photodetector 5 is positioned to detect reflected light 12 when such reflection occurs. The output of photodetector 5 is fed to null detector 6. Although only rudimentary elements are shown to better demonstrate the principle involved more sophisticated apparatus is of course within the purview of the invention and would normally be used in practice.

In operation as a device for measuring angular velocity disc member 3 is initially stationary and light source 4 is positioned such that light beam 15 impinges on the peripheral surface of the disc at an angle that satisfies the Brewster angle requirement for no reflection. Photodetector 5, of course, has no output and Null detector 6 indicates a null condition. Subsequent rotation of rotatable shift 11 by motor 9 violates the Brewster angle requirement causing reflected light 12 to activate photodetector 5. The output of photodetector 5 is indicated by null detector 6. Light source 4 is then moved a distance d or d that results in the Brewster Angle requirement again being met with the consequent elements of reflected light 12. In practice it is merely necessary to move the light source back and fourth until null detector 6 indicates a null condition. The distance light source 4 has been moves is determined from calibrated scale 8 and is a measure of the angular velocity of the disc member (and the rotatable shaft).

When used as a device for determining light beam incidence angle the light source 4 is in a fixed position and disc member 3 and its associated components are remotely located (in a spacecraft for instance). Disc member 3 is again initially stationary and positioned such that light beam 15 intercepts its peripheral surface at the Brewster angle. As long as the attitude of the equipment remains the same with respect to the light beam, no reflected light will be detected by photodetector 5 and null detector 6 will indicate a null condition. When the attitude changes however, and the light beam strikes the disc at a new angle reflected light 12 occurs and the null detector indicates that deviation has occurred. Disc member 3 is then rotated at various velocities until a velocity that eliminates the reflected light is achieved. This velocity is indicated by tachometer 10 and is a direct measure of the angle of deviation from the fixed light beam 15.

While the invention has been described is one presently preferred embodiment, it is understood that the words which have been used are words of description rather than words of limitation and that changes within tory material,

rotating said rotatable member,

detecting light reflected from said disc member,

changing the angle of incidence of said light beam to an angle 0 at which light is no longer reflected from said disc member, and

converting the change in angle of incidence of said light beam into an angular velocity measurement of said rotatable member in accordance with the relationship tan 0 y tan 0 (1 V/C sin 0 

1. The method of measuring angular velocity of a rotatable member comprising the steps of: mounting a disc member of refractory material on said rotatable member, projecting a light beam that is linearly polarized in its plane of incidence onto the peripheral surface of said disc member at an angle theta 1, whose tangent equals the relative index of refraction of the refractory material, rotating said rotatable member, detecting light reflected from said disc member, changing the angle of incidence of said light beam to an angle theta 2 at which light is no longer reflected from said disc member, and converting the change in angle of incidence of said light beam into an angular velocity measurement of said rotatable member in accordance with the relationship tan theta 2 y tan theta 1 (1 + V/C sin theta 1). 